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The Nature of All Things: E = mc2

by
Scope Correspondent

It’s plastered on coffee mugs, bumper stickers, and t-shirts. There is a thirteen-foot statue of it in central Berlin. People rattle it off when trying to sound impressive. It has become synonymous with genius. It is the most well-known physics equation in the world. I’m talking, of course, about E = mc2, Albert Einstein’s most lasting contribution to the popular conception of physics.

But given its ubiquity, it’s surprisingly hard to define. Most people can’t answer the question of what exactly this equation means, other than that it’s sometimes called the “relativity equation.” It’s very neat and clean on paper, but deceptively so; behind those few symbols is a revolutionary way of understanding our universe that allowed science and society at large to develop in ways that would have been unfathomable without it.

Let’s say that we’re using E = mc2 to describe something familiar, like a duck. First, we need to know what the symbols are telling us about this duck. If you were to translate those symbols into words, the equation reads, “Energy is equal to mass times the speed of light, squared.” E stands for the total amount of energy in an object or system; in this case, the duck’s body. The sound energy in the duck’s quack, the thermal energy that keeps its body temperature regulated, the kinetic energy that’s produced when it flaps its wings, all of that is contained within E. The m refers to the duck’s mass, or how much matter it’s made up of. The average duck consists of about a kilogram of mass. The third symbol in the equation, c, is the speed of light. Because light travels so fast, c is a very big number—671 million miles per hour. What’s even more incredible is that in this equation the speed of light is squared, meaning you have to multiply it by itself. That number is 449 with fifteen zeroes after it.

Because energy and mass are on opposite sides of the equal sign, the equation expresses something called “mass-energy equivalence,” which says that mass can be converted into energy, and energy into mass; they are two forms of the same thing. So, what does it mean if our duck’s mass is multiplied by such an astronomically (pun fully intended) large number? The presence of the huge c2 tells us that even a tiny amount of mass can produce a lot of energy.

The most obvious example of this amazing conversion is a nuclear bomb. The most powerful one, a Russian hydrogen bomb detonated in 1961, started with less than 2 ounces of matter.  But when much of that matter fully converted into energy, the resulting explosion released 60 megatons’ worth of energy (the bomb dropped on Hiroshima was a paltry .02 megatons), enough to obliterate Paris and all of its suburbs. If we were to convert the one kilogram, or 35 ounces, of our duck into pure energy in the same way, it could produce an explosion of 1,050 megatons, large enough to wipe out the entire island of Cyprus. That’s one dangerous duck.

Thankfully for us, most energy is locked away in ways that make it difficult to release in pure form, especially in systems as complicated as ducks. It’s easier when working with individual particles, especially when antimatter is involved. Antimatter is the opposite of matter; particles of antimatter have the same mass as their matter cousins, but their charges, spin and other properties are reversed. This might not sound important (we have left and right hands that are opposites of each other, after all), but whenever a particle of matter meets a particle of its corresponding antimatter, the two particles are annihilated; that is, they disappear completely and are converted into light, or pure energy. When this phenomenon was discovered in 1932, it confirmed our famous equation’s prediction that mass and energy were indeed interchangeable.

That interchangeability means that the equation can go the opposite direction too, and that energy can be converted into mass. It’s given us such mind-bending technology as particle accelerators, like the Large Hadron Collider. The LHC sends beams of high-energy protons speeding toward each other at 99.99% of the speed of light. Again, this is because of that pesky c2 in the equation; huge amounts of energy are needed to produce small amounts of mass. When the protons collide, their kinetic energy is converted into tens to hundreds of new particles, most of which are very short-lived and decay almost immediately back into pure energy, or light. However, some of them stick around—electrons, protons, positrons and antiprotons—and are analyzed using the LHC’s giant detectors. That’s like shooting two ducks at each other at very high speeds and seeing a shower of geese, swans and loons (and possibly, for a blip of an instant, Toucan Sam) pop into existence when they collide. Voilà. Matter from energy.

If it sounds strange, that’s because it is. E = mc2 completely changed how we understand our universe. We don’t think about it very often in our daily lives, because of the extreme numbers involved. The most obvious expressions of the mass-energy equivalence happen at very tiny scales and involve very large amounts of energy. However, applications of E = mc2 are everywhere. Much of the technology that we use today is powered by it: radioactivity, another expression of mass being converted into energy, is the source of PET scans, smoke detectors and radiocarbon dating. The sun is steadily converting its mass into the heat and light that sustains our planet through a series of nuclear reactions. And maybe, somewhere, two ducks have just collided and produced a chicken.

Comments

1 Comment
Very useful information
April 4, 2014 at 8:25 am

I think this is very useful information